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Register a new userStress chain analysis of soil particles in slope via persistent homology
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The relationship between the macroscopic response of the slope and the macrostructure of the force chain network under the action of the metal plate was studied by the particle discrete element method and the persistent homology. The particle accumulation model was used to simulate the instability process of slope under the continuous downward action of metal plate by the particle discrete element method. The macroscopic responses such as the total velocity vector of the two-dimensional slope deposit, the angle of the slip cracking surface when the slope is unstable, and the average velocity in the y-direction of the slope were studied. Then, the normal force chain undirected network model of the natural accumulation of slope stacking particles was constructed. Finally, the topological characteristics of the particle contact force chain network of the slope top were analyzed by the persistent homology method to obtain the barcode. Finally, the relationship between the instability evolution and the characteristics of persistent homology is established. This research provides a new method for the study of slope instability topology identification. Thus, the instability destruction of slope can be predicted effectively.
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Using software UDEC to simulate the instability failure process of slope under seismic load, studing the dynamic response of slope failure, obtaining the deformation characteristics and displacement cloud map of slope, then analyzing the instability state of slope by using the theory of persistent homology, generates bar code map and extracts the topological characteristics of slope from bar code map. The topological characteristics corresponding to the critical state of slope instability are found, and the relationship between topological characteristics and instability evolution is established. Finally, it provides a topological research tool for slope failure prediction. The results show that the change of the longest Betti 1 bar code reflects the evolution process of the slope and the law of instability failure. Using discrete element method and persistent homology theory to study the failure characteristics of slope under external load can better understand the failure mechanism of slope, provide theoretical basis for engineering protection, and also provide a new mathematical method for slope safety design and disaster prediction research.
We introduce a homology-based technique for the analysis of multiqubit state vectors. In our approach, we associate state vectors to data sets by introducing a metric-like measure in terms of bipartite entanglement, and investigate the persistence of homologies at different scales. This leads to a novel classification of multiqubit entanglement. The relative occurrence frequency of various classes of entangled states is also shown.
New representations of tree-structured data objects, using ideas from topological data analysis, enable improved statistical analyses of a population of brain artery trees. A number of representations of each data tree arise from persistence diagrams that quantify branching and looping of vessels at multiple scales. Novel approaches to the statistical analysis, through various summaries of the persistence diagrams, lead to heightened correlations with covariates such as age and sex, relative to earlier analyses of this data set. The correlation with age continues to be significant even after controlling for correlations from earlier significant summaries
Inspired by topological data analysis techniques, we introduce persistent homology observables and apply them in a geometric analysis of the dynamics of quantum field theories. As a prototype application, we consider simulated data of a two-dimensional Bose gas far from equilibrium. We discover a continuous spectrum of dynamical scaling exponents, which provides a refined classification of nonequilibrium universal phenomena. A possible explanation of the underlying processes is provided in terms of mixing wave turbulence and vortex kinetics components in point clouds. We find that the persistent homology scaling exponents are inherently linked to the geometry of the system, as the derivation of a packing relation reveals. The approach opens new ways of analyzing quantum many-body dynamics in terms of robust topological structures beyond standard field theoretic techniques.
The particle discrete element simulation of the instability and failure process of the granular slope accumulator model when the metal plate continues downward is obtained, and the two-dimensional total velocity vector of soil particle velocity and slope slip during the instability and failure of the slope accumulator are obtained. Macro-response processes such as removing the angle of the crack surface and the average velocity in the y-direction of the slope top of the slope accumulation body. Construct a normal force chain undirected network model of the slope accumulation body particles under natural accumulation, and study the location of its slip surface, and The results are compared with the experimental results. Finally, the complex network method is used to analyze the topological characteristics of the contact force chain network of the particles on the slope top of the slope accumulation body, and the average degree, clustering coefficient and average shortest path are obtained during the slope instability of the slope accumulation body. The evolutionary rule of the method is used to verify its accuracy in combination with the strength reduction method. The research results show that the average shortest path can provide a more effective early warning of the instability and failure of slope deposits. A complex network theory is used to study the macro response of the slope deposits and its force chain. The interrelationship between the macroscopic structure of the network provides a new mathematical analysis method for the study of slope instability.
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